Presentation On Analytical Characteristics of Bangladesh
By Division
Submitted toM. Amir Hossain, Ph.D.Professor, Applied StatisticsD.U.East West University, Bangladesh.
H.M. Faisal Ahmed 2010-2-91-021
Submitted By
Group C
Data Presentation We have collected demographic data from BBS
(Bangladesh Bureau of Statistics) website www.bbs.gov.bd/Home.aspx. We decided to collect two types of data (Qualitative & Quantitative). For Qualitative data we have considered the data about the Land Area, and number of Male and Female in a division and for quantitative data we have considered the data about age. We have applied the data in different types of Data Presentation techniques.
Bar Chart Histogram Frequency Polygon Cumulative Frequency Curve
The Bar chart and Histogram are based on the following fact table:
Based on Enumerated population in 2011
DIVISION AREA MALE FEMALE
BARISAL 13,645 4,006,000 4,140,000
CHITTAGONG 33,771 13,763,000 14,361,000
DHAKA 30,989 23,814,000 22,915,000
RAJSHAHI 34,495 9,183,000 9,146,000
KHULNA 22,285 7,782,000 7,781,000
SYLHET 12,596 4,882,000 4,925,000
A bar chart or bar graph is a way of showing information by the lengths of a set of bars. The bars are drawn horizontally or vertically. If the bars are drawn vertically, then the graph can be called a column graph or a block graph. A chart which displays a set of frequencies using bars of equal width whose heights are proportional to the frequencies.
In our presentation the height of the bars represents the number of different individuals, the X axis represents different division and Y axis the number of individuals.
Chart 01: Bar Chart of Male and Female per Division
14
34
31
34
22
13
0
5
10
15
20
25
30
35
40
Thousands
Land Area (SquareKillometer)
Chart 2: Bar Chart of Land Area per Division
A graphical representation, similar to a bar chart in structure, that organizes a group of data points into user-specified ranges. The histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins. In statistics, a histogram is a graphical display of tabulated frequencies, shown as bars. It shows what proportion of cases fall into each of several categories: it is a form of data binning. The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent. The intervals are generally of the same size.
Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable.
Chart 04: Histogram of Male & Female per Division
Chart 05: Histogram of Land Area per Division
A frequency polygon is a graphical display of a frequency table. The intervals are shown on the X-axis and the number of scores in each interval is represented by the height of a point located above the middle of the interval (Class Mark). The points are connected so that together with the X-axis they form a polygon.
In our presentation Class Marks (Class Mid Points) are plotted through X axis and Number of individuals in that class are plotted through Y axis.
Frequency Distribution Table (With class Mark)
Class Class Mark Frequency
40-44 42 7133824
45-49 47 5152206
50-54 52 4322404
55-59 57 2774265
60-64 62 2662799
64-69 67 1758685
70-74 72 1461443
Class Class Mark Frequency
00-04 2 14465810
05-09 7 16534124
10-14 12 15704322
15-19 17 12186950
20-24 22 10688351
25-29 27 9858549
30-34 32 9363144
35-39 37 8198944
-2
46
810
1214
1618
- 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Age
Po
pu
lati
on
Nu
mb
er
Millions
Chart 06: Frequency Polygon of peoples age Information of Bangladesh
Also known as an ogive, this is a curve drawn by plotting the value of the first class on a graph. The next plot is the sum of the first and second values, the third plot is the sum of the first, second, and third values, and so on. The total of a frequency and all frequencies below it in a frequency distribution.
In our presentation cumulative frequency of age groups is plotted through Y axis and Class Frequency through Class Mark is plotted through X axis.
Class Class Mark FrequencyCumulative
Frequency
00-04 2 14465810 14465810
05-09 7 16534124 30999935
10-14 12 15704322 46704257
15-19 17 12186950 58891207
20-24 22 10688351 69579559
25-29 27 9858549 79438108
30-34 32 9363144 88801253
35-39 37 8198944 97000197
Class Class Mark FrequencyCumulative
Frequency
40-44 42 7133824 104134021
45-49 47 5152206 109286228
50-54 52 4322404 113608632
55-59 57 2774265 116382897
60-64 62 2662799 119045696
64-69 67 1758685 120804382
70-74 72 1461443 122265825
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Age
Po
pu
lati
on
Nu
mb
ers
Millions
Chart 07: Cumulative Frequency Curve of Age Information of Bangladesh
The Assignment was done within short time that’s why there might be some errors in our analysis but still the data will be able to visualize the actual picture.
MEASURES OF DISPERSIONMEASURES OF DISPERSION
The descriptive statistics that measure the quality of scatter are called measures of dispersion. Measures of dispersion give a more complete picture of the data set. It deals with spread of data. A small value of the measure of dispersion indicates that data are clustered closely. A large value of dispersion indicates the estimate of central tendency is not reliable.
TYPES OF MEASURES OF TYPES OF MEASURES OF DISPERSIONDISPERSION
There are many type of measurement of dispersion, here we discuss as below-
Absolute Measures of Dispersion:
These measures give us an idea about the amount of dispersion in a set of observations. They give the answers in the same units as the units of the original observations. When the observations are in kilograms, the absolute measure is also in kilograms. If we have two sets of observations, we cannot always use the absolute measures to compare their dispersion. We shall explain later as to when the absolute measures can be used for comparison of dispersion in two or more than two sets of data. The absolute measures which are commonly used are:
1. Range2. Mean Deviation3. Variance4. Standard Deviation
Relative Measure of Dispersion:
These measures are calculated for the comparison of dispersion in two or more than two sets of observations. These measures are free of the units in which the original data is measured. If the original data is in dollar or kilometers, we do not use these units with relative measure of dispersion. These measures are a sort of ratio and are called coefficients. Each absolute measure of dispersion can be converted into its relative measure. Hear we only discuses:
1. Coefficient of Variance
For ungroup data: The simplest measure of dispersion is the range. The range is calculated by simply taking the difference between the maximum and minimum values in the data set.
Range=Highest Value-Lowest Value
For group data: If there are group data than the range is calculated by taking the difference between the upper limit of the highest class and the lower limit of the lowest class.
Range= upper limit of the highest class- lower limit of the lowest class.
MEAN DEVIATIONMEAN DEVIATION
The mean deviation is the first measure of dispersion that we will use that actually uses each data value in its computation. It is the mean of the distances between each value and the mean. It gives us an idea of how spread out from the center the set of values is.
For ungroup data:
For group data:
MDX X
n
f
|XX|f MD
I I
VARIANCEVARIANCE
Variance is a mathematical expression of the average squared deviations from the mean. We can said also, the arithmetic mean of the squares of the deviations of all values in a set of numbers from their arithmetic mean.
Population Variance:
_ Sample Variance:
2
2
( )X
N
1
)( 22
n
XXS
Working formula for population variance is:
Working formula for sample variance is:
22
2 )(N
X
N
X
1
)(
S
22
2
nnX
X
The usual measure of dispersion cannot be used to compare the dispersion if the units are different, even the unit are same but the means are different.
It reports variation relative to the mean. It is useful for comparing distributions with
different units.
Hear we only discuses:
1. Coefficient of Variation
The CV is the ratio of the standard deviation to the arithmetic mean, expressed as a percentage. We can also said, to compare the variations (dispersion) of two different series, relative measures of standard deviation must be calculated. This is known as co-efficient of variation.
The formula of CV is given bellow:
100X
sCV
Class Interval Frequency X/Midpoint xf -- -- --f
00-0405-0910-1415-1920-2425-2930-3435-3940-4445-4950-5455-5960-6465-6970-74
14.4616.5315.7012.1810.689.859.368.197.135.154.322.772.661.751.46
27
12172227323742475257626772
28.92115.78188.4207.06234.96265.95299.52303.03299.46242.05224.64157.89164.92117.25105.12
-22.18-17.18-12.18-7.18-2.182.827.82
12.8217.8222.8227.8232.8237.8242.8247.82
22.1817.1812.187.182.182.827.82
12.8217.8222.8227.8232.8237.8242.8247.82
320.72283.98191.2287.4523.6827.7773.19
104.99127.05117.52120.1890.91
100.6074.9369.81
491.95295.15148.3551.554.757.95
61.15164.35317.55520.75773.95
1077.151430.351833.552286.75
7113.594878.822329.09627.8750.7378.30
572.3641346.022264.132681.863343.462983.703804.733208.713338.65
122.19 2954.95 1814 38700.32
XX || XX || XX 2XX 2XXf
Range= 74-0 = 74_ X= 2954.95/122.19= 24.18
_Mean Deviation= = 1814/122.19=14.8457 f
||f
XX
Determination of the year 2011:Figure in “Mil”
Variance, =38700.32/122.19= 316.72
Standard Deviation=
= 17.7966
Coefficient of Variance (CV)= = (17.7966/24)X100
= 74.15%
f
XXS
2
1
)( 22
n
XXSS
100X
sCV
122.19
38700.32
Helps to take decision and identifying the nature of business and economic decisionsHelpful in identifying the nature of relationship among many business and economic variablesOne variable depends on another and can be determined by it
The Coefficient of Correlation (r) is a measure of the strength of the relationship between two variables.It requires interval or ratio-scaled data (variables). It can range from -1.00 to 1.00.Values of -1.00 or 1.00 indicate perfect and strong correlation.Values close to 0.0 indicate no linear correlation.Negative values indicate an inverse relationship and positive values indicate a direct relationship
X Y
X- X^ Y-Y^ (X-X^)(Y-Y^) (X-X^)2 (Y-Y^)2
3 41
-2 -14 28 4 196
7 762 21 42 4 441
6 561 1 1 1 1
5 78
0 23 0 0 529
2 43
-3 -12 36 9 144
1 34
-4 -21 84 16 441
X^ = 5 Y^ = 55
(X-X^)(Y-Y^)=191
X-X^)2 = 34 (Y-Y^)2
= 1752
r = 0.78
Comment: As, the value or ‘r’ is positive , so the variables have stronger relation between them.
A regression is a statistical analysis assessing the association between two variables. It is used to find the relationship between two variables.General form of linear regression model Y = a + bX + eWhere,
Y : dependent variable a : intercept term b : slope of the line
X : independent variable e : error termWant to estimate a and b such that ∑e2 is minimum
X YX- Ẋ Y- Ȳ (X- Ẋ)(Y- Ȳ) (X- Ẋ)2
3 41 -2 -14 28 4
7 76 2 21 42 4
6 56 1 1 1 1
5 78 0 23 0 0
2 43 -3 -12 36 9
1 34-4 -21 84 16
Ẋ= 5 Ȳ= 55
(X- Ẋ)(Y- Ȳ)
=191
(X- Ẋ)2 = 34
So,Here after putting the value,
= 191/34 = 5.6
a = 55 - 5.6(5) =27 Form the linear regression model, Y = 27 + 5.6X Here regression coefficient is 5.6 that means if we change 1 unit of independent variable, dependent variable will change 5.6.
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